Deriving Average Energy Function For A Classical DOF

[Bashyboy]

Hello everyone,

The problem I am currently working is exactly what is given in this link: https://www.physicsforums.com/showthread.php?t=554243

However, I do not understand why we integrate between 0 and infinity. What is the motivation for doing so?

 

[dextercioby]

It's because of the absolute value of c. You have no reason to consider negative c's, since the absolute value will cancel the integration.

 

[Bashyboy]

Do you perhaps mean the absolute value of q?

 

[BvU]

Yes.
The result Steve writes blows up at minus infinity (if c>0), so the integral is not 0 at all: it doesn't exist.
That's because he omitted the | | .
E = c |q| can be integrated. From minus infinity to 0 is exactly the same as from 0 to infinity.

 

[paranormal]

Hello,

The motivation for integrating between 0 and infinity in this case is to account for all possible energies that the classical degree of freedom (DOF) can have. By integrating from 0 to infinity, we are considering all possible values of energy, from the lowest possible value (0) to the highest possible value (infinity). This allows us to accurately calculate the average energy of the DOF, as it takes into account the entire range of possible energies. Additionally, integrating from 0 to infinity is a common approach in classical mechanics and statistical mechanics, as it allows us to consider all possible states of a system. I hope this helps clarify the reasoning behind this approach.